\( \mathrm{ABCD} \) is a trapezium in which \( \mathrm{AB} \| \mathrm{CD} \) and \( \mathrm{AD}=...

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\( \mathrm{ABCD} \) is a trapezium in which \( \mathrm{AB} \| \mathrm{CD} \) and \( \mathrm{AD}=\mathrm{BC} \) (see Fig. \& Show that
(i) \( \angle \mathrm{A}=\angle \mathrm{B} \)
(ii) \( \angle \mathrm{C}=\angle \mathrm{D} \)
-(iii) \( \triangle \mathrm{ABC} \cong \triangle \mathrm{BAD} \)
_(iv) diagonal \( \mathrm{AC}= \) diagonal \( \mathrm{BD} \)
[Hint: Extend \( \mathrm{AB} \) and draw a line through \( \mathrm{C} \) parallel to \( \mathrm{DA} \) intersecting \( \mathrm{AB} \) produced at \( \mathrm{E} \).]
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